People who are not subjects can have honorary knighthoods, but they can't call themselves Sir.

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My first Canadian passport contained the phrase "A Canadian citizen is a British Subject" but my current one no longer says that. This may have changed in 1982 when the Trudeau government introduced the Constitution Act that lead to full political independence from the UK. Canada still regards the Queen as sovereign, but it is likely just ceremonial at this point.

Regardless of the history, the convention is that the Prime Minister has to approve the honors. I believe the convention is also that the Prime Minister notapprove the requests - as is well-known, Conrad Black disavowed his Canadian citizenship so he could get his honors.